Neither term is ‘more logical’; they mean the opposite of each other, just as they are expressed, nor do they necessarily mean ‘one cares very little’.

I care (x amount); I couldn’t care less than I do if I wanted to. I’m incapable of it.

I care (x amount), but I could care less than I do.

Either one is lazy usage when the speaker/writer really means ‘I don’t give a sh*t.’

I suppose griping about it amounts to airing out a pet peeve, but we have to have something to do with our time, eh?

I think it is too deeply entrenched in the language now, though hopefully, there will always be some of us who know the difference. Sigh ….

“Hopefully” describes actions; “Hopeful” describes people.

“Hopefully” is an adverb, which means that it can describe verbs, adjectives, and other adverbs. Consider this sentence.

“Hopefully, Bob ran to the store.”

In this sentence, “hopefully” describes “ran.” Bob’s running is characterized by hope. This is similar to writing “Quickly, Bob ran to the store.” In this sentence, “hopefully” is used correctly.

However, “hopefully” is frequently misused to describe a person’s attitude about a future event. Consider this sentence.

“Hopefully, the store will be open.”

This is wrong. In this sentence, we are not trying to describe the manner in which the store is open. Instead, we are trying to describe how we feel about the store being open. In short, we are hopeful. Because we are describing ourselves, we need to use the adjective “hopeful,” not the adverb “hopefully.” Here are two ways to write this correctly:

“We are hopeful that the store will be open.”
“We hope that the store will be open.”

The first correction uses the adjective “hopeful” to describe “we.” I prefer the second sentence, which uses the action verb “hope” instead of the weak verb “are” plus the adjective “hope.”